1. Field of the Invention
This invention relates to a method of reducing noise produced by motors and to the motors produced by this method, and more particularly to a method of tuning the natural frequency of a rotor and to motors incorporating such tuned rotors.
2. Description of the Prior Art
When the natural frequency of a rotor in an induction motor is close to a harmonic of the input frequency of the supply voltage (e.g., for 60 Hz, the first harmonic is 120 Hz, the third harmonic is 240 Hz, and the successive odd harmonics are 360 Hz, 480 Hz, etc.), unwanted noise and vibration can be generated. There is a correlation between rotor natural frequency and motor noise.
Three speed motors have been used in washing machines for a number of years and have provided very satisfactory service. Several, seemingly small, adjustments were recently made to manufacturing methods for these motors, including the use of an interlock rotor lamination system, use of counterbore laminations for manufacturing convenience, and stack height control through measurement rather than lamination counting. As these adjustments were introduced, a rather noticeable change occurred in the sounds emitted from the motors We shall refer to this sound as "bearing knock."
Bearing knock is a phenomena that occurs when cyclical forces on the rotor system cause sufficient movement in the bearing clearance to move the shaft from one end of the clearance to the other. The knocking sound that is heard is the impacting of the shaft on the bearing surface. The problem of bearing knock is most severe when the speed of rotation is low, because bearing oil film thickness and damping is at its lowest in this situation. At higher speeds, the bearing film thickness increases, the stiffness decreases, and the damping increases. Bearing knock is of lesser severity as higher speeds because of these more favorable conditions.
Bearing knock is affected by two major factors, the first of which is electromagnetic imbalance in the rotor that causes a side-to-side force on the rotor. Causes that contribute to such imbalance are dynamic air gap variation due to rotor eccentricity, or defective rotor conductor bars. The second major factor affecting bearing knock is the system response to the forcing mechanism. If the forcing mechanism drives the system close to the natural frequency of the rotor/shaft system, the vibrational amplitude will become amplified. Small changes in the construction of a rotor, such as changes from lose lamination construction to interlock construction, may shift the natural frequency of the rotor/shaft system enough to cause an objectional amplification of vibration.
To better understand the nature of the problem and the inventive solution, it is helpful to consider the response of an undamped rotor-mass spring system, which is modelled schematically as a simple forced vibration system in FIG. 8. This model comprises the mass of rotor 100, a spring comprising the shaft 12 and bearings 102 and 102', and a driver comprising unbalanced rotor forces F. In the model, we shall assume that the unbalanced rotor forces are mostly electromagnetic forces, and that the excitation is sinusoidal.
The equation of motion for this system in one of the planes of motion is given by: EQU my+ky=F.sub.0 sin .omega.t
where m=the mass of the rotor;
k=the shaft/rotor stiffness; PA1 F.sub.0 =the amplitude of the driver force; PA1 y=the displacement from the rest state; and PA1 .omega.=the driver frequency, in radians per second.
This expression may be solved for y to give a steady-state result: ##EQU1## where ##EQU2## is the natural frequency of the rotor.
The response of this system depends on the magnitude of the forcing function, the stiffness of the shaft, and the ratio of the driving to the natural frequency. The vibration is in the form of a sinusoidal motion. Usually, only the amplitude of this motion is of interest, and this amplitude is expressed as: ##EQU3##
This maximum displacement is plotted in FIG. 9 for a number of different values of F.sub.o /k as a function of the natural frequency .omega..sub.n divided by the excitation frequency .omega.. FIG. 9 shows that the vibrational amplitude increases rapidly as the excitation frequency gets closer to the natural frequency of the rotor-shaft system. It also shows that the amplitude increase as the driving function increases. When a system vibrates at the natural frequency, it is said to resonate. Very little energy is required to keep the vibrational amplitude large. The vibrations of the rotor mass are restrained by the bearing system. If the amplitude of the vibration is large at the rotor, it will lead to large forces at the bearing. This, in turn, allows the shaft to move within the bearing clearance, and cause bearing knock.
The noise and vibration that occurs due to resonance in the rotor system can be reduced or eliminated either by changing the mass of the rotor, changing the distance between bearing centers, or changing the shaft stiffness. However, construction constraints may limit the range of options. For example, the rotor mass can be changed only within size constraints of the rotor. Only limited amounts of material can be removed if the electrical properties and strength of the rotor are to remain the same. Also, the distance between rotor bearings may be constrained by material cost and the application in which the motor is used. In addition, it may be impractical to change the shaft stiffness by substituting a shaft having a different diameter throughout its entire length because a different diameter shaft may require the use of nonstandard bearing sizes and may increase machining costs.
Counterboring of rotor laminations for "hot dropped" rotors is known. This manufacturing technique involves heating a stack of rotor laminations so that they expand and can easily accommodate a shaft, and then "hot dropping" them onto the shaft. As the rotor stack cools, it shrinks onto the shaft. Compressive forces resulting from this shrinkage hold the laminations onto the rotor shaft. For manufacturing convenience, it was found to be advantageous to counterbore some of the outer laminations of the stack so that the stack of laminations could be more easily dropped onto the shaft. However, because attention had not been given to the change in natural frequency caused by the counterboring, and because the source of the noise was not fully known, many motors using "hot dropped" rotors proved unsatisfactorily noisy, and the practice of counterboring outer laminations was limited. Furthermore, no "press-on" rotors (i.e., rotors made by pressing a stack of rotors onto a shaft without the aid of a relative temperature difference between the rotor stack and the shaft) are known to have used counterbored laminations for noise control.
In view of all of the above, it would be advantageous to provide motors that avoid increased noise due to bearing knock. It would further be advantageous to provide a method for adjusting the natural frequency of rotor systems in motors in a manufacturing environment without substantially altering the size, weight, or electrical properties of the motor.